Q_T-RESUMMATION FOR POLARIZED SEMI-INCLUSIVE DEEP INELASTIC SCATTERING

Abstract

We study the transverse-momentum distribution of hadrons produced in semiinclusive deep-inelastic scattering. We consider cross sections for various combinations of the polarizations of the initial lepton and nucleon or the produced hadron, for which we perform the resummation of large double-logarithmic perturbative corrections arising at small transverse momentum. We present phenomenological results for the process ep → eπX for the typical kinematics in the COMPASS experiment. We discuss the impact of the perturbative resummation and of estimated non-perturbative contributions on the corresponding cross sections and their spin asymmetry.Semi-inclusive deep inelastic scattering (SIDIS) with polarized beams and target, ep → ehX, for which a hadron h is detected in the final state, has been a powerful tool for investigating the spin structure of the nucleon. It also challenges our understanding of the reaction mechanisms in QCD. The bulk of the SIDIS events provided by experiments are in a kinematic regime of large virtuality Q 2 of the exchanged virtual photon and relatively small transverse momentum q T . In our recent paper 1 , we have studied the transverse-momentum dependence of SIDIS observables in this region, applying the resummation technique of 2 . The processes we considered were the leading-twist double-spin reactions: (i) Here arrows to the right (upward arrows) denote longitudinal (transverse) 1 October 25, 2018 13:15 Proceedings Trim Size: 9in x 6in dis2006 2polarization. Needless to say, the final-state pion could be replaced by any hadron. The same is true for the Λ, as long as the observed hadron is spin-1/2 and its polarization can be detected experimentally. Here we present a brief summary of the main results of 1 .There are five Lorentz invariants for SIDIS, e(k)the center-of-mass energy squared for the initial electron and the proton,which is orthogonal to both p A and p B . To write down the cross section, we use a frame where p A and q are collinear, and we call the azimuthal angle between the lepton plane and the hadron plane φ. In this frame, the transverse momentum of the final-state hadron B with respect to p A and q is given by p T = z f q T .The lowest-order (LO) cross section differential in q T (or p T ) is of O(α s ) and has been derived in 3 . It can be decomposed into several pieces with different dependences on φ:for processes (i) and (ii) in (1),for (iv) and (v), andfor (iii). Here Φ A (Φ B ) is the azimuthal angle of the transverse spin vector of A (B) as measured from the hadron plane around p A ( p B ) in the so-called hadron frame for which q = (0, 0, 0, −Q). At small q T , σ 0 and σ T 0 develop the large logarithmic contribution α s ln(Q 2 /q 2 T )/q 2 T . At yet higher orders, corrections as large as α k s ln 2k (Q 2 /q 2 T )/q 2 T arise in the cross section. We have worked out the NLL resummation of these large logarithmic corrections in σ 0 and σ T 0 for all the processes in (1) within the b-space resummation formalism of 2 , extending the previous studies on the resumm...